Finite Group Databasebeta

← C2×#24919951 #36282986

Subgroups — C2×#24919951 #36282986

Order 21248.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128406C211yesmaximal, characteristic, complemented
2C2×#19128398C211yesmaximal, characteristic
3#24919951C2116yesmaximal, direct product factor
4C2×#19128109C211yesmaximal, characteristic, complemented
5C2×#19128038C211yesmaximal, characteristic, complemented
6C2×#19128018C211yesmaximal, characteristic, complemented
7C2×#19128043C211yesmaximal, characteristic, complemented
8C2×#19128007C211yesmaximal, characteristic, complemented
9C2×#19127979C211yesmaximal, characteristic, complemented
10C2×#19127945C211yesmaximal, characteristic, complemented
11C2×#19127929C211yesmaximal, characteristic, complemented
12C2×#19127798C211yesmaximal, characteristic, complemented
13C2×#19127775C211yesmaximal, characteristic, complemented
14C2×#19127741C211yesmaximal, characteristic, complemented
15C2×#107×D83C211yesmaximal, characteristic, complemented
16C2×#480×C83C211yesmaximal, characteristic, complemented
17C22×#13050578C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128406—24no—
21#19128406C2218yescomplemented
22#19128398—24no—
23#19128398C2218yes—
24C2×#14581791C2211yescharacteristic
25C2×#14581785—21no—
26C2×#14581783C2211yescharacteristic
27C2×#14581782—21no—
28C2×#14581773—21no—
29C2×#14581772C2211yescharacteristic
30C2×#14581771—21no—
31C2×#14581771C2211yescharacteristic
32C2×#14581770—21no—
33C2×#14581763—21no—
34C2×#14581763C2211yescharacteristic
35C2×#14581757C2211yescharacteristic
36C2×D4×Dic83C2211yescharacteristic
37C2×C4×C22⋊D83—21no—
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×(C22⋊D83)⋊C4—21no—
40C2×#14581751C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43#19128109C2218yescomplemented
44#19128043C2218yescomplemented
45#19128038C2218yescomplemented
46#19128018C2218yescomplemented
47#19128007C2218yescomplemented
48#19127979C2218yescomplemented
49#19127945C2218yescomplemented
50#19127929C2218yescomplemented
51#19127798C2218yescomplemented
52#19127775C2218yescomplemented
53#19127741C2218yescomplemented
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58#107×D83C2218yescomplemented
59C2×#14581724C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×#14581723C2211yescharacteristic
62C2×Dic83⋊C8C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581715C2211yescharacteristic
66C2×#14581713C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69C2×#121×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic
71#480×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×C22⋊D83—21no—
80C22×C22⋊D83D411yescharacteristic
81C23×Dic83—21no—
82C22×C4×D83—21no—
83C22×C4×D83—21no—
84C22×C4×D83C2311yescharacteristic
85C2×#13050578—24no—
86C2×#13050578C2314yes—
87C2×#13050574—24no—
88C2×#13050574C2314yes—
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91C2×C8×D83—24no—
92C2×C8×D83C2314yes—
93#14581791—22no—
94#14581791C2314yes—
95#14581785—28no—
96#14581783—22no—
97#14581783C2314yes—
98#14581782—28no—
99#14581773—28no—
100#14581772—22no—
101#14581772C2314yes—
102#14581771—28no—
103#14581771—22no—
104#14581771C2314yes—
105#14581770—28no—
106#14581763—28no—
107#14581763—22no—
108#14581763C2314yes—
109#14581757—22no—
110#14581757C2314yes—
111D4×Dic83—22no—
112D4×Dic83C2314yes—
113C4×C22⋊D83—28no—
114C4×C22⋊D83D414yes—
115C4×C22⋊D83C2314yes—
116(C22⋊D83)⋊C4—28no—
117#14581751—22no—
118#14581751C2314yes—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4D411yescharacteristic
131C4⋊C4×D83—22no—
132C4⋊C4×D83—22no—
133C4⋊C4×D83C2314yes—
134C4⋊C4×D83C2314yes—
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83D411yescharacteristic
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4D411yescharacteristic
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83C2311yescharacteristic
145#14581726C2314yes—
146#14581725C2314yes—
147#14581725C2314yes—
148#14581725C2314yes—
149#14581724C2314yes—
150#14581723C2314yes—
151#14581723C2314yes—
152Dic83⋊C8C2314yes—
153#14581717C2314yes—
154#14581717C2314yes—
155#14581715C2314yes—
156#14581713C2314yes—
157(C2×D83)⋊C8C2314yes—
158#14581702C2314yes—
159C22×D4×C83—21no—
160C22×D4×C83C2311yescharacteristic
161C23×C4×C83—21no—
162C23×C4×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C22×C8×C83C2311yescharacteristic
165#121×C83—22no—
166#121×C83C2314yes—
167C2×C4⋊C4×C83—22no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83C2314yes—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C22⋊C4×C83—21no—
174#107×C83C2314yes—
175#107×C83C2314yes—
176#102×C83C2314yes—
177#102×C83C2314yes—
178C22⋊C8×C83C2314yes—
179C23×D83C2×D411yescharacteristic
180C2×Dic166—22no—
181C2×Dic166—22no—
182C2×Dic166—21no—
183C2×Dic166—24no—
184C2×Dic166—82no—
185C2×Dic166C2412yes—
186C2×C22⋊D83—24no—
187C2×C22⋊D83—24no—
188C2×C22⋊D83—44no—
189C2×C22⋊D83C2×D414yes—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—24no—
195C22×Dic83—82no—
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C2×C4×D83—22no—
200C2×C4×D83—22no—
201C2×C4×D83—24no—
202C2×C4×D83—24no—
203C2×C4×D83—82no—
204C2×C4×D83—82no—
205C2×C4×D83C2×D412yes—
206C2×C4×D83C2412yes—
207#13050578—28no—
208#13050574—28no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8#4114yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C8×D83—28no—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—21no—
217C4⋊Dic83—24no—
218C4⋊Dic83—24no—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221C4⋊Dic83C2412yes—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4C2×D414yes—
229C22⋊Dic83—24no—
230C22⋊Dic83—24no—
231C22⋊Dic83—24no—
232C22⋊Dic83—24no—
233C22⋊Dic83C2×D414yes—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4C2×D414yes—
236C4×Dic83—24no—
237C4×Dic83—24no—
238C4×Dic83C2×D412yes—
239C4×Dic83C2412yes—
240C24×C83—21no—
241C24×C83C2×D411yescharacteristic
242C2×D4×C83—24no—
243C2×D4×C83—21no—
244C2×D4×C83—22no—
245C2×D4×C83—22no—
246C2×D4×C83—82no—
247C2×D4×C83C2412yes—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—24no—
254C22×C4×C83—82no—
255C22×C4×C83C2×D412yes—
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2412yes—
258C22×C4×C83C2411yescharacteristic
259C2×C8×C83—22no—
260C2×C8×C83—22no—
261C2×C8×C83C2412yes—
262C2×C8×C83C2412yes—
263C4⋊C4×C83—24no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83—21no—
267C4⋊C4×C83C2412yes—
268C4⋊C4×C83C2412yes—
269C4⋊C4×C83C2412yes—
270C22⋊C4×C83—24no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—42no—
276C23×C83—42no—
277C23×C83—42no—
278C23×C83C22×D412yes—
279C23×C83C22×D411yescharacteristic
280C22×D83—22no—
281C22×D83—22no—
282C22×D83#13714yes—
283C22×D83C22×D412yes—
284D4×C83—22no—
285D4×C83—22no—
286D4×C83—42no—
287D4×C83—84no—
288C2×C4×C83—22no—
289C2×C4×C83—24no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—42no—
296C2×C4×C83—42no—
297C2×C4×C83—42no—
298C2×C4×C83—84no—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D411yescharacteristic
301C2×C4×C83C2×#4112yes—
302C2×C4×C832−1+412yes—
303C2×C4×C83C2511yescharacteristic
304C22⋊D83—28no—
305C22⋊D83—48no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—42no—
314C2×Dic83—42no—
315C2×Dic83—42no—
316C2×Dic83—42no—
317C2×Dic83—84no—
318C2×Dic83C22×D412yes—
319C2×Dic83C22×D412yes—
320C2×Dic83C22×D412yes—
321C4×D83—24no—
322C4×D83—22no—
323C4×D83—22no—
324C4×D83—84no—
325C4×D83—84no—
326Dic166—22no—
327Dic166—22no—
328Dic166—42no—
329Dic166—84no—
330C8×C83—22no—
331C8×C83—22no—
332C83⋊C8—22no—
333C83⋊C8C2×#4114yes—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—22no—
337C22×C83—44no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—84no—
342C22×C83#54712yes—
343C22×C83C2×#13712yes—
344C22×C83#57612yes—
345C22×C83C23×D411yescharacteristic
346C2×D83—28no—
347C2×D83—22no—
348C2×D83—22no—
349C2×D83C2×#13714yes—
350C4×C83—22no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83#54712yes—
355C4×C83C22×#4111yescharacteristic
356C4×C83C2×2−1+411yescharacteristic
357Dic83—22no—
358Dic83—22no—
359Dic83—22no—
360Dic83—42no—
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364C2×#3346—831nomaximal, Sylow
365C2×C83—42no—
366C2×C83—82no—
367C2×C83#334614yescomplemented
368C2×C83C2×#54711yescharacteristic
369C2×C83C22×#13711yescharacteristic
370C2×C83C2×#57611yescharacteristic
371D83—24no—
372C2×#554—831no—
373C2×#553—831no—
374#3346—8316no—
375C2×#501—831no—
376C2×#484—831no—
377C2×#481—831no—
378C2×#485—831no—
379C2×#480D8311yescharacteristic, complemented
380C2×#479—831no—
381C2×#474—831no—
382C2×#468—831no—
383C2×#465—831no—
384C2×#440—831no—
385C2×#435—831no—
386C2×#428—831no—
387C22×#107—831no—
388C83C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—831no—
390C22×M16—831no—
391C23×C8—831no—
392#554—838no—
393#554—1664no—
394#553—838no—
395#553—1664no—
396C2×C4⋊Q8—831no—
397C2×#126—1661no—
398C2×#125—831no—
399C2×#125—1661no—
400C2×#123—1661no—
401C2×C22⋊Q8—831no—
402C2×C22⋊Q8—831no—
403C2×C22⋊Q8—1661no—
404C2×C22⋊Q8—1661no—
405C2×#121—831no—
406C2×#121—1661no—
407C2×#121C2×D8311yescharacteristic
408C2×C4×Q8—831no—
409C2×C4×D4—831no—
410C2×C4×D4—831no—
411C2×C4×D4—1661no—
412C2×C4×D4—1661no—
413C2×#117—831no—
414C22×C4⋊C4—831no—
415C22×C4⋊C4—831no—
416C22×C4⋊C4C2×D8311yescharacteristic
417#501—838no—
418#485—838no—
419#484—838no—
420#481—838no—
421#480C2×D8318yescomplemented
422#479—838no—
423#474—838no—
424#468—838no—
425#465—838no—
426#440—838no—
427#435—838no—
428#428—838no—
429C2×#107—831no—
430C2×#107—831no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—838no—
434C2×#107C2×D8311yescharacteristic
435C2×#107C2×D8311yescharacteristic
436C2×#106—831no—
437C2×#106—831no—
438C2×#106—831no—
439C2×C4⋊C8—831no—
440C2×#103—831no—
441C2×#103—831no—
442C2×#103—831no—
443C2×#102—831no—
444C2×#102C2×D8311yescharacteristic
445C2×#102C2×D8311yescharacteristic
446C2×C22⋊C8—831no—
447C2×C22⋊C8C2×D8311yescharacteristic
448C2×#97—831no—
449C22×Q8—831no—
450C22×Q8—1661no—
451C22×D4—21no—
452C22×D4—831no—
453C22×D4—1661no—
454C22×D4C22×D8311yescharacteristic
455C23×C4—21no—
456C23×C4—831no—
457C23×C4—1661no—
458C23×C4—1661no—
459C23×C4—1661no—
460C23×C4C22×D8311yescharacteristic
461C2×SD16—834no—
462C2×SD16—1664no—
463C2×M16—834no—
464C2×M16—1664no—
465C22×C8—831no—
466C22×C8—831no—
467C22×C8—834no—
468C22×C8—1664no—
469C22×C8C22×D8311yescharacteristic
470C22×C8C22×D8311yescharacteristic
471C4⋊Q8—834no—
472C4⋊Q8—1662no—
473#126—1668no—
474#125—834no—
475#125—1662no—
476#125—1668no—
477#123—1668no—
478C22⋊Q8—834no—
479C22⋊Q8—834no—
480C22⋊Q8—1668no—
481C22⋊Q8—1668no—
482C22⋊Q8—1662no—
483C22⋊Q8—1662no—
484#121—22no—
485#121—834no—
486#121—1662no—
487#121—1668no—
488#121C22×D8314yes—
489C4×Q8—834no—
490C4×Q8—1662no—
491C4×D4—834no—
492C4×D4—834no—
493C4×D4—834no—
494C4×D4—1662no—
495C4×D4—1668no—
496C4×D4—1668no—
497#117—834no—
498#117—1662no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—1662no—
508C2×C4⋊C4—1662no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C4⋊C4C22×D8311yescharacteristic
520C2×C4⋊C4C22×D8314yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—831no—
523C2×C22⋊C4—831no—
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C42—831no—
530C2×C42—1661no—
531C2×C42—1661no—
532#107—834no—
533#107—834no—
534#107—834no—
535#107—834no—
536#107C22×D8314yes—
537#107C22×D8314yes—
538#106—834no—
539#106—834no—
540#106—834no—
541C4⋊C8—834no—
542#103—834no—
543#103—834no—
544#103—834no—
545#102—834no—
546#102C22×D8314yes—
547#102C22×D8314yes—
548C22⋊C8—834no—
549C22⋊C8C22×D8314yes—
550#97—834no—
551C24—21no—
552C24—831no—
553C24D4×D8311yescharacteristic
554C2×Q8—832no—
555C2×Q8—6642no—
556C2×Q8—1664no—
557C2×Q8—1662no—
558C2×Q8—1662no—
559C2×Q8—1661no—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—82no—
565C2×D4—3324no—
566C2×D4—834no—
567C2×D4—1664no—
568C2×D4—1664no—
569C2×D4C23×D8312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—831no—
578C22×C4—831no—
579C22×C4—831no—
580C22×C4—832no—
581C22×C4—832no—
582C22×C4—6642no—
583C22×C4—6642no—
584C22×C4—6642no—
585C22×C4—1664no—
586C22×C4—1664no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1664no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4D4×D8312yes—
595C22×C4D4×D8311yescharacteristic
596C22×C4C23×D8312yes—
597C22×C4C23×D8311yescharacteristic
598SD16—1668no—
599M16—1668no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—834no—
603C2×C8—832no—
604C2×C8—832no—
605C2×C8—1668no—
606C2×C8—1662no—
607C2×C8C23×D8312yes—
608C2×C8C23×D8312yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—834no—
614C4⋊C4—832no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—1664no—
618C4⋊C4—1664no—
619C4⋊C4—1664no—
620C4⋊C4—1664no—
621C4⋊C4—1664no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1661no—
625C4⋊C4—1661no—
626C4⋊C4—1661no—
627C4⋊C4—1664no—
628C4⋊C4C23×D8312yes—
629C4⋊C4C23×D8312yes—
630C4⋊C4C23×D8312yes—
631C22⋊C4—24no—
632C22⋊C4—834no—
633C22⋊C4—834no—
634C22⋊C4—1664no—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C42—832no—
640C42—832no—
641C42—1664no—
642C42—1664no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—834no—
651C23—832no—
652C23—1662no—
653C23—1662no—
654C23C2×D4×D8312yes—
655C23C2×D4×D8311yescharacteristic
656Q8—3322no—
657Q8—6644no—
658Q8—1662no—
659Q8—1662no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664D4—3328no—
665D4—1668no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—3322no—
678C2×C4—3322no—
679C2×C4—3322no—
680C2×C4—3322no—
681C2×C4—832no—
682C2×C4—832no—
683C2×C4—832no—
684C2×C4—6644no—
685C2×C4—6644no—
686C2×C4—6644no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1664no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4C2×D4×D8312yes—
698C2×C4C2×D4×D8311yescharacteristic
699C2×C4#41×D8312yes—
700C2×C4#1458183912yes—
701C2×C4C24×D8311yescharacteristic
702C8—22no—
703C8—22no—
704C8—834no—
705C8—1662no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—834no—
715C22—1662no—
716C22—1662no—
717C22—1668no—
718C22#1912834912yes—
719C22#137×D8312yes—
720C22#1912850212yes—
721C22C22×D4×D8311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—3322no—
727C4—3322no—
728C4—3322no—
729C4—3322no—
730C4—1662no—
731C4—1662no—
732C4—1662no—
733C4#1912834912yes—
734C4C2×#41×D8311yescharacteristic
735C4C2×#1458183911yescharacteristic
736C2—42no—
737C2—82no—
738C2—1664no—
739C2#2491995114yesdirect product factor
740C2C2×#1912834911yescharacteristic
741C2C2×#137×D8311yescharacteristic
742C2C2×#1912850211yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#480×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128398C2
hypercenterC2×#480D83
hypocenterC83C2×#3346
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19128406C2semidirect
3. #24919951C2direct (N × H)
4. C2×#19128109C2semidirect
5. C2×#19128038C2semidirect
6. C2×#19128018C2semidirect
7. C2×#19128043C2semidirect
8. C2×#19128007C2semidirect
9. C2×#19127979C2semidirect
10. C2×#19127945C2semidirect
11. C2×#19127929C2semidirect
12. C2×#19127798C2semidirect
13. C2×#19127775C2semidirect
14. C2×#19127741C2semidirect
15. C2×#107×D83C2semidirect
16. C2×#480×C83C2semidirect
21. #19128406C22semidirect
43. #19128109C22semidirect
44. #19128043C22semidirect
45. #19128038C22semidirect
46. #19128018C22semidirect
47. #19128007C22semidirect
48. #19127979C22semidirect
49. #19127945C22semidirect
50. #19127929C22semidirect
51. #19127798C22semidirect
52. #19127775C22semidirect
53. #19127741C22semidirect
58. #107×D83C22semidirect
71. #480×C83C22semidirect
367. C2×C83#3346semidirect
379. C2×#480D83semidirect
388. C83C2×#3346semidirect
421. #480C2×D83semidirect
739. C2#24919951direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191284062
C2×#191283982
#249199512
C2×#191281092
C2×#191280382
C2×#191280182
C2×#191280432
C2×#191280072
C2×#191279792
C2×#191279452
C2×#191279292
C2×#191277982
C2×#191277752
C2×#191277412
C2×#107×D832
C2×#480×C832
C2×#334683